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  <div class="section" id="numpy-random-randomstate-triangular">
<h1>numpy.random.RandomState.triangular<a class="headerlink" href="#numpy-random-randomstate-triangular" title="Permalink to this headline">¶</a></h1>
<p>method</p>
<dl class="method">
<dt id="numpy.random.RandomState.triangular">
<code class="sig-prename descclassname">RandomState.</code><code class="sig-name descname">triangular</code><span class="sig-paren">(</span><em class="sig-param">left</em>, <em class="sig-param">mode</em>, <em class="sig-param">right</em>, <em class="sig-param">size=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.RandomState.triangular" title="Permalink to this definition">¶</a></dt>
<dd><p>Draw samples from the triangular distribution over the
interval <code class="docutils literal notranslate"><span class="pre">[left,</span> <span class="pre">right]</span></code>.</p>
<p>The triangular distribution is a continuous probability
distribution with lower limit left, peak at mode, and upper
limit right. Unlike the other distributions, these parameters
directly define the shape of the pdf.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>New code should use the <code class="docutils literal notranslate"><span class="pre">triangular</span></code> method of a <code class="docutils literal notranslate"><span class="pre">default_rng()</span></code>
instance instead; see <em class="xref py py-obj">random-quick-start</em>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>left</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Lower limit.</p>
</dd>
<dt><strong>mode</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>The value where the peak of the distribution occurs.
The value must fulfill the condition <code class="docutils literal notranslate"><span class="pre">left</span> <span class="pre">&lt;=</span> <span class="pre">mode</span> <span class="pre">&lt;=</span> <span class="pre">right</span></code>.</p>
</dd>
<dt><strong>right</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Upper limit, must be larger than <em class="xref py py-obj">left</em>.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape.  If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn.  If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">left</span></code>, <code class="docutils literal notranslate"><span class="pre">mode</span></code>, and <code class="docutils literal notranslate"><span class="pre">right</span></code>
are all scalars.  Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(left,</span> <span class="pre">mode,</span> <span class="pre">right).size</span></code>
samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized triangular distribution.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.random.Generator.triangular.html#numpy.random.Generator.triangular" title="numpy.random.Generator.triangular"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Generator.triangular</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The probability density function for the triangular distribution is</p>
<div class="math">
<p><img src="../../../_images/math/44c727b0ace7fa5e79aa8b0293e54afb0490c7b2.svg" alt="P(x;l, m, r) = \begin{cases}
\frac{2(x-l)}{(r-l)(m-l)}&amp; \text{for $l \leq x \leq m$},\\
\frac{2(r-x)}{(r-l)(r-m)}&amp; \text{for $m \leq x \leq r$},\\
0&amp; \text{otherwise}.
\end{cases}"/></p>
</div><p>The triangular distribution is often used in ill-defined
problems where the underlying distribution is not known, but
some knowledge of the limits and mode exists. Often it is used
in simulations.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r66e8bd10eee2-1"><span class="brackets">1</span></dt>
<dd><p>Wikipedia, “Triangular distribution”
<a class="reference external" href="https://en.wikipedia.org/wiki/Triangular_distribution">https://en.wikipedia.org/wiki/Triangular_distribution</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Draw values from the distribution and plot the histogram:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">h</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">triangular</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span>
<span class="gp">... </span>             <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-RandomState-triangular-1.png" src="../../../_images/numpy-random-RandomState-triangular-1.png" />
</div>
</dd></dl>

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